Permutations.

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Presentation transcript:

Permutations

Factorials How can we arrange 5 students in a line to go to lunch today? _________ __________ __________ __________ ________

Factorials Definition: The product of integers from 1 to n. For Example: How many ways can I arrange the letters in the word APRIL?

n is the total and r is the amount chosen Permutation An arrangement or listing of objects where order IS important. n is the total and r is the amount chosen

Permutations ORDER MATTERS! Placement Examples: assigned seats, winning a race or running a race, 1st place, 2nd place, etc Positions Examples: President, Vice President, Secretary, Treasure Specific job/chore Examples: Hand out markers, pass out papers, etc

Permutations Simplify each expression. a. 12P2 b. 10P4 12 • 11 = 132 c. At a school science fair, ribbons are given for first, second, third, and fourth place, There are 20 exhibits in the fair. How many different arrangements of four winning exhibits are possible? 12 • 11 = 132 10 • 9 • 8 • 7 = 5,040 = 20P4 = 20 • 19 • 18 • 17 = 116,280

Permutations Example There are 50 runners in a race. How many different ways can the runners finish in 1st, 2nd, or 3rd?

Permutations Example A president and vice president are being chosen from a group of 20 people. How many ways can this be done?

Calculator

Permutations Examples w/ Calculator  Your band has written 11 songs & plans to record 5 of them for a CD. In how many ways can you arrange the songs on the CD? In how many ways can you arrange 4 of the letters in the word PANTHER?

Combinations

List ALL the possible ways of writing the letters A, B, C, & D in pairs.

n is the total and r is the amount chosen Combination A selection of objects where order is NOT important. n is the total and r is the amount chosen

Combinations Example How many different ways are there to select two class representatives from a class of 20 students?

Combinations Example For your school pictures, you can choose four backgrounds from a list of ten. How many combinations of backgrounds are possible?

Combinations Example You order a pizza at a restaurant. You can choose 3 toppings from a list of 12. How many combinations of toppings are possible?

Find Probability There are 28 students in your math class. Your teacher chooses 5 students at random to complete a group project. Find the probability that you and your best friend are chosen to work in the group.

Solution The number of possible outcomes The number of favorable outcomes with both of you in it. Probability = 2,600/98,280 = 5/189

Find Probability A student council has 16 members, including 4 seniors. There are 4 members randomly chosen to represent the student council at a school open house. What is the probability that all 4 council members chosen are seniors?

Permutation or Combination? Mike is picking 4 of his 12 friends to go to the Braves game with him. How many ways can he pick the 4 friends that go with him?

Permutation or Combination? How many ways can you arrange 4 of the letters in the word PANTHER?

Permutation or Combination? Mr. Wagner needs 3 people from my class of 15 to come help clean up the gym. How many ways can I pick the 3 kids?

HW textbook p. 345 #1 – 3, 5 – 7, 25 p. 349 #7 – 10, #17-20